2013/11/30 by Mohammed Abouzaid, Ivan Smith · 2 citations
Mathematics · #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Compactification (mathematics) #Equivariant cohomology #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Quantum cohomology #Symplectic geometry #Symplectic manifold #math.GT #math.SG #msc:53D40 #msc:57M25
paper · pdf · doi:10.1215/00127094-3449459
published as Duke Math. J. 165, no. 6 (2016), 985-1060 · 58 pages, 15 figures. Final version: minor corrections
arxiv created 2015/10/19 · openalex publication_date 2016/01/28 · arxiv updated 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology over fields of characteristic zero. The key ingredient is the construction of a degree-one Hochschild cohomology class on a Floer A∞-algebra associated to the (k,k)-nilpotent slice Yk obtained by counting holomorphic discs which satisfy a suitable conormal condition at infinity in a partial compactification Y¯k. The space Y¯k is obtained as the Hilbert scheme of a partial compactification of the A2k−1-Milnor fiber. A sequel to this paper will prove formality of the symplectic cup and cap bimodules and infer that symplectic Khovanov cohomology and Khovanov cohomology have the same total rank over characteristic zero fields.